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Scalable single-mode surface-emitting laser via open-Dirac singularities


Single-aperture cavities are a key component of lasers that are instrumental for the amplification and emission of a single light mode. However, the appearance of high-order transverse modes as the size of the cavities increases has frustrated efforts to scale-up cavities while preserving single-mode operation since the invention of the laser six decades ago1,2,3,4,5,6,7,8. A suitable physical mechanism that allows single-mode lasing irrespective of the cavity size—a ‘scale invariant’ cavity or laser—has not been identified yet. Here we propose and demonstrate experimentally that open-Dirac electromagnetic cavities with linear dispersion—which in our devices are realized by a truncated photonic crystal arranged in a hexagonal pattern—exhibit unconventional scaling of losses in reciprocal space, leading to single-mode lasing that is maintained as the cavity is scaled up in size. The physical origin of this phenomenon lies in the convergence of the complex part of the free spectral range in open-Dirac cavities towards a constant governed by the loss rates of distinct Bloch bands, whereas for common cavities it converges to zero as the size grows, leading to inevitable multimode emission. An unconventional flat-envelope fundamental mode locks all unit cells in the cavity in phase, leading to single-mode lasing. We name such sources Berkeley surface-emitting lasers (BerkSELs) and demonstrate that their far-field corresponds to a topological singularity of charge two, in agreement with our theory. Open-Dirac cavities unlock avenues for light–matter interaction and cavity quantum electrodynamics.

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Fig. 1: Scalable open-Dirac electromagnetic cavity and the Berkeley surface-emitting laser.
Fig. 2: Quantization of the band structure in open-Dirac cavities forming higher-order modes and evidence for an unconventional fundamental mode with a flat envelope.
Fig. 3: Complex frequency scaling of open-Dirac electromagnetic cavities.
Fig. 4: Lasing characteristics of BerkSELs erasing higher-order modes around the open-Dirac singularity.
Fig. 5: Far-field scaling of BerkSELs and photon statistics.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

The computer codes that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


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This research was mostly supported by the Office of Naval Research (ONR) Young Investigator Award (N00014-19-1-2737), the ONR JTO MRI Award (N00014-20-1-2752), the ONR grant N00014-20-1-2723 and the National Science Foundation (NSF) Career Award (ECCS-1929659). It was partially supported by the Laboratory Directed Research and Development Program of Lawrence Berkeley National Laboratory (LBNL) under US Department of Energy contract no. DE-AC02-05CH11231, the NSF QLCI programme through grant number OMA-2016245, the Moore Inventor Fellows programme and the Bakar Fellowship at UC Berkeley. The work was partially performed at the UC Berkeley Marvel Nanofabrication Laboratory, the Molecular Foundry at LBNL and the San Diego Nanotechnology Infrastructure, a member of the National Nanotechnology Coordinated Infrastructure, which is supported by the National Science Foundation (ECCS-1542148). We thank M. Montero for technical assistance regarding fabrication.

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Authors and Affiliations



B.K. conceived the project, proposed the idea, and guided the theoretical and experimental investigations. R.C. performed the theoretical calculations. W.N. fabricated the devices. W.R. performed the measurements. W.Q., E.M., S.D. and A.S. contributed to the fabrication of the larger-size devices requested by the reviewers. All authors contributed to discussions and R.C, W.R. and B.K. wrote the manuscript.

Corresponding author

Correspondence to Boubacar Kanté.

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The Regents of the University of California have filed a patent application (US provisional application 63/304,581) on technology related to the processes described in this article.

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Nature thanks Alejandro Martinez and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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This file contains Supplementary Sections A–J, including Supplementary Table 1, Figs. 1–18 and References.

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Contractor, R., Noh, W., Redjem, W. et al. Scalable single-mode surface-emitting laser via open-Dirac singularities. Nature 608, 692–698 (2022).

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